Method for cutting involute gears

ABSTRACT

A method for simultaneously cutting and chamfering involute gears. The pressure angle α 1  and module M of the teeth of a hob for cutting the teeth are selected with respect to the nominal pressure angle α 0  and nominal module m of the gear to be cut according to the following equation: m cos α 0  =M cos α 1 . According to the present invention, a single hob cutter is sufficient to cut gears having a wide range of numbers of teeth.

TECHNICAL FIELD

The present invention relates to a method for cutting gears,particularly to a method for cutting an involute gear and simultaneouslychamfering its addendum.

BACKGROUND ART

In conventional hob cutters for cutting involute gears having chamferedtooth profiles, the pressure angle exhibited by the rack of teeth on thehob, the "hob tooth profile," is the same as the nominal pressure angleof the gear to be formed. It is also known to reduce the pressure angleon the hob tooth profile to "preshave" the gear tooth profile. In bothcases, the relation between the number of teeth on the gear to be cutand the appropriate chamfering value varies monotonously andcontinuously, such that the rate of such variation is relatively largewhere the number of teeth is relatively small.

In other words, prior hob cutters have been designed to optimally cut agear having a particular number of teeth. If a gear having more thanthis particular number of teeth is cut, the chamfer will be increased.On the other hand, if a gear having fewer teeth than this particularnumber is cut with the same hob cutter, the chamfer will decrease ordisappear.

Accordingly, in the prior art, one of several different hob cutters wasselected responsive to the number of teeth on the gear to be cut, inorder to appropriately chamfer the teeth of the gear.

SUMMARY OF THE INVENTION

It is an object of the present invention to overcome the above-describeddisadvantages of the prior art and to provide a single hob cutter forcutting involute gears, whereby a range of gears widely varying innumber of teeth can all be chamfered properly.

The above-described object can be achieved by a hob cutter according tothe present invention, the hob cutter comprising a cutting edgeconsisting of a first rack tooth profile portion, for cutting a maintooth profile portion, and a second rack tooth profile portion forchamfering an addendum portion, characterized in that the pressure angleα₁ of the first rack tooth profile portion is larger than the pressureangle α₀ of the gear to be cut, that the pressure angle α₂ of the secondrack tooth profile portion is larger than the pressure angle α_(c) atthe pitch circle diameter (PCD) of a second involute portion of thegear, i.e., the chamfer, and that the above-mentioned factors aredetermined according to the following general formula:

    m cos α.sub.0 =M cos α.sub.1

where M is the module of the hob cutter, and m is the module of the gearto be cut.

The angles α₂ and α_(c) are similarly related.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a partial enlarged sectional view of one embodiment of a hobcutter for cutting involute gears according to the present invention,showing the structure of the tooth portion;

FIG. 2 is a partial enlarged sectional view showing comparable exampleof prior art hob cutters;

FIG. 3 is a graph showing the relation between the number of teeth onthe gear to be cut and the appropriate chamfering values (expressed as afunction of the module) of the hob cutter according to the presentinvention (Curve A), and the corresponding relation between the numberof teeth and the chamfering values of the prior art hob cutter (CurveB), respectively; and

FIG. 4 is a graph showing the relation between the number of teeth andchamfering values of a gear of module m=4, pressure angle α₀ =20°, whichis achieved according to the present invention.

PREFERRED EMBODIMENT OF THE INVENTION

In FIG. 1 and FIG. 2, α₁ is the pressure angle of a first rack toothprofile portion of a hob cutter for cutting involute gears according tothe present invention, and α₁ ' is the pressure angle of a first racktooth profile portion of the prior art hob cutter, which in the priorart was equal to α₀, the pressure angle of the gear to be cut. α₂ is thepressure angle of a second rack tooth profile portion in the hob cutteraccording to the present invention, for cutting the chamfer on the teethof the gear at an angle α_(c), and α₂ ' is the pressure angle of thesecond rack tooth profile portion of the prior art hob cutter, which wasequal to α_(c), the pressure angle of the chamfered portion of the gear.

In the hob cutter for cutting involute gears according to the presentinvention, the pressure angle α₁ of the first rack tooth profile portionof the hob cutter is larger than the pressure angle α₀ of the gear to becut, and similarly, the pressure angle α₂ of the second rack toothprofile portion is larger than the pressure angle α_(c) of the chamferedportion of the gear. These values are determined in accordance with thefollowing general formula:

    m cos α.sub.0 =M cos α.sub.1

where M is the module of the hob cutter, and m is the module of the gearto be cut.

α₂ and α_(c) are similarly related according to the modules of the hoband the gear.

As discussed above, prior art hob cutters were formed in such a mannerthat the pressure angle α₁ ' of the first rack tooth profile portion wasequal to the pressure angle α₀ ' of the gear to be formed, while α₂ ' ofthe second rack tooth profile portion was equal to the desired pressureangle α_(c) on the pitch circle diameter (PCD) of the second involutecurve, that is, the chamfered portion of the gear. Accordingly, therelation between the number of teeth of the gear to be cut and thechamfer values for a particular hob has a low value for gears having aminimum number of teeth, and is then a monotonously increasing function,as shown by Curve B in FIG. 3. This fact prevented the prior art hobcutter to cut the chamfer at the preferred angle α_(c) ' (correspondingto a chamfering value of 0.1, expressed as a function of the module andshown by the horizontal line) unless the number of teeth of the gear tobe cut was relatively large. If the prior art hob cutter did notcorrespond to the number of teeth on the gear to be formed, the chamferwas excessively large or small, or did not exist. Typically, three hobswere required to cut gears having tolerable but non-ideal tooth formsand between 15 and 80 teeth.

According to the present invention, however, as described above, therelation between the chamfering values and the number of teeth does notvary greatly from the nominal value of 0.1 of the module (indicated bythe horizontal line) as shown by Curve A in FIG. 3, so that a single hobcutter can properly cut and chamfer gears having widely varying numbersof teeth.

FIG. 4 shows the relation between the number of teeth and the chamferingvalues for a typical gear having module m=4 and the pressure angle α₀=20°, wherein the ordinate represents the chamfering value, and theabscissa represents the number of teeth. The chamfering value is, again,expressed as a function of the module, so that the 0.4 ideal value forthe chamfer for a gear of module m=4 is equivalent to the 0.1 value ofFIG. 3.

According to the invention, a single hob cutter can chamfer gears havingbetween 15 and 80 teeth, the chamfering values being within ±0.05 mm ofthe ideal. Such errors are fully tolerable. As shown by intersection ofthe curve with the 0.4 chamfering line at the points marked Z₁ and Z₂,when the number of teeth is 19 or 65, the chamfering value correspondsexactly with the standard value of 0.4. This curve thus shows thataccording to the present invention, a single hob cutter havingappropriate module M can be used successfully to cut gears of thecorresponding module m and a wide range of numbers of teeth.

INDUSTRIAL APPLICABILITY

When the hob cutter according to the present invention is used to cut agear, the relation between the chamfering values and the number of teethis not a monotonously increasing function of the number of teeth on thegear, but increases to a maximal value and than decreases, as shown inFIG. 4; moreover, the optimal chamfering value is obtained for twodifferent numbers of teeth Z₁ and Z₂. Therefore, the range of the numberof teeth which can be cut by means of a single hob cutter is extremelylarge, and a single hob cutter is sufficient to cut almost all gears.

What is claimed is:
 1. A method for cutting an involute gear having amodule m and a pressure angle α₀, said method comprising the step of:gradually cutting the teeth of the gear to be formed from a gear blank,using a hob of module M and pressure angle α₁, wherein the modules ofthe hob and the gear to be cut and the respective pressure angles arerelated by the following equation: m cos α₀ =M cos α₁.
 2. The method ofclaim 1, wherein the teeth of the gear to be cut are to have formedthereon a chamfer defined by an angle α_(c), the hob having a portionfor cutting said chamfer defined by an angle α₂, wherein these anglesare related by the following equation: m cosα_(c) =M cos α₂.
 3. Themethod of claim 1 wherein the number of teeth on the gear which can becut by a particular hob varies over a range between about 15 and about80 teeth.